Problem: Divide. Write your answer in simplest form. $ \dfrac{5}{3} \div \left(-\dfrac{6}{7}\right) = {?} $
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $-\dfrac{6}{7}$ is $-\dfrac{7}{6}$. Therefore: $ \dfrac{5}{3} \div \left(-\dfrac{6}{7}\right) = \dfrac{5}{3} \times \left(-\dfrac{7}{6}\right) $ $ \phantom{\dfrac{5}{3} \div \left(-\dfrac{6}{7}\right)} = \dfrac{5 \times (-7)}{3 \times 6} $ $ \phantom{\dfrac{5}{3} \div \left(-\dfrac{6}{7}\right)} = -\dfrac{35}{18} $